Establishment of Information Physics based on algebraic geometry

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Almost all learning machines used in information science are singular because they have degenerate Fisher Information matrices. Regular statistical theory can not be applied to singular learning machines. In this research, we established new information physics theory for singular learning machines based on higher dimensional algebraic geometry, and clarified that the asymptotic behaviors of generalization and training errors are determined by two birational invariants. Based on new theory, we derived a widely applicable information criterion, by which the generalization error can be estimated from training error in both singular and regular learning machines.